cobs-ts v1.0.3

COBS-TS

A TypeScript implementation of Constrained B-Splines (COBS), based on the R package cobs.

Description

COBS-TS provides qualitatively constrained (regression) smoothing splines via linear programming and sparse matrices. It supports various constraints including:

• Monotonicity (increasing/decreasing)
• Convexity/Concavity
• Periodicity
• Pointwise constraints

Installation

npm install cobs-ts

Usage

import { Cobs } from 'cobs-ts';

// Example 1: Basic spline fitting
const x = [1, 2, 3, 4, 5];
const y = [1.1, 2.3, 2.9, 3.8, 4.2];

const cobs = new Cobs();
const result = cobs.fit(x, y);
console.log(result.fitted);      // Fitted values
console.log(result.knots);       // Knot locations
console.log(result.coefficients); // Spline coefficients

// Evaluate at a specific point
const value = result.evaluate(2.5);

// Example 2: Fitting with constraints
const constrainedResult = cobs.fit(x, y, {
    constraints: [
        { type: 'monotone', increasing: true },  // Monotone increasing
        { type: 'pointwise', x: 3, y: 3, operator: '>=' }  // Point constraint
    ],
    degree: 2,
    numKnots: 10,
    lambda: 0.5
});

// Access the fit results
console.log(constrainedResult.fitted);      // Fitted values
console.log(constrainedResult.residuals);   // Residuals
console.log(constrainedResult.coefficients); // Spline coefficients

// Evaluate derivatives
const derivative = constrainedResult.evaluateDerivative(2.5);
const secondDerivative = constrainedResult.evaluateSecondDerivative(2.5);

Features

• B-spline basis functions of degree 1 or 2
• Multiple constraint types
• Automatic knot selection
• Information criterion (AIC, BIC, SIC) for model selection
• Sparse matrix implementation for efficient computation
• Support for weighted fitting
• Quantile regression capability

API

Cobs.fit(x: number[], y: number[], options?: CobsOptions): CobsResult

Main function for fitting constrained B-splines.

Options

• constraint: 'none' | 'increase' | 'decrease' | 'convex' | 'concave' | 'periodic'
• weights: number[] - Observation weights
• knots: number | number[] - Number of knots or explicit knot locations
• degree: 1 | 2 - Degree of B-spline basis
• tau: number - Quantile level (default: 0.5 for median regression)
• lambda: number | null - Smoothing parameter
• ic: 'AIC' | 'BIC' | 'SIC' - Information criterion for model selection
• pointwise: PointwiseConstraint[] - Additional pointwise constraints
• maxiter: number - Maximum number of iterations
• nknots: number - Number of knots if not explicitly specified
• keep: boolean - Whether to keep additional fitting information

Development

# Install dependencies
npm install

# Build
npm run build

# Run tests
npm test

# Run linter
npm run lint

License

GPL-2.0-or-later (matching the original R package license)

References

• Original R package by Pin T. Ng and Martin Maechler
• He, X. and Ng, P. (1999): "COBS: Qualitatively Constrained Smoothing via Linear Programming"; Computational Statistics, 14, 315-337.